6x(x+3)=60

Solution for 6x(x+3)=60 equation:

Simplifying
6x(x + 3) = 60

Reorder the terms:
6x(3 + x) = 60
(3 * 6x + x * 6x) = 60
(18x + 6x2) = 60

Solving
18x + 6x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + 18x + 6x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 18x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-10 + 3x + x2) = 0

Factor a trinomial.
6((-5 + -1x)(2 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-5, 2}